Pascoe's Theorem is a result in geometry that deals with the properties of certain configurations of points and lines. Specifically, it states that if you have a triangle and a point inside it, the segments connecting the point to the vertices of the triangle can be used to create a new triangle. This new triangle has specific relationships to the original triangle, particularly in terms of area and angles. The theorem is often used in the study of triangle geometry and can help in solving problems related to concurrent lines and centroids. It provides a way to understand how points within a triangle can influence its overall properties, making it a useful tool for mathematicians and students alike.